论文标题
$ ϕ_ {n} $和$ψ_{n}^{2} $在椭圆曲线上点的最大常见估值
The greatest common valuation of $ϕ_{n}$ and $ψ_{n}^{2}$ at points on elliptic curves
论文作者
论文摘要
给定一个椭圆曲线的最小模型，$ e/k $，在有限的扩展名中，$ k $，$ {\ mathbb q} _ {p} _ {p} _ {p} $对于任何有理prime，$ p $，$ p $，以及任何点$ p \ in e（k）in Infinite订单中的任何点$ p \ in Infinite Order，我们确定了准确的$ \ \ min $ \ min \ weft（p） \ left（ψ_{n}^{2}（p）\ right）\ right）$，其中$ v $是$ k $和$ k $和$ ϕ_ {n}（p）$和$ψ_{n}（n}（p）$的归一化估值。
Given a minimal model of an elliptic curve, $E/K$, over a finite extension, $K$, of ${\mathbb Q}_{p}$ for any rational prime, $p$, and any point $P \in E(K)$ of infinite order, we determine precisely $\min \left( v \left( ϕ_{n}(P) \right), v \left( ψ_{n}^{2}(P) \right) \right)$, where $v$ is a normalised valuation on $K$ and $ϕ_{n}(P)$ and $ψ_{n}(P)$ are polynomials arising from multiplication by $n$ for this model of the curve.
